Would there even be any noticeable difference on Earth? Would it have any affect on tides, the lunar orbit, how seasons changed, or what the pull of gravity is on earth? How would it affect other planets in the solar system?

I'm not an expert, but I do have basic orbital mechanics knowledge... here's my best educated answer.

Even though we are technically in an elliptical orbit around the sun, it is a very "circular" elliptical orbit. This question becomes increasingly complicated when you start factoring in the effect it would have on other planets and more elliptical paths.

The short answer is, not really. We are 150 million km away from the sun and are tiny in size. Having an Earth on the other side of our orbital path would essentially negate any "wobble" the sun and Earth already don't have due to the massive difference in mass.

If our orbital path had a vastly different eccentricity and was severely elliptical, then it's possible that the other Earth would get close enough at perigee and apogee that the orbit would be affected over time.